25 potentoal titration the first and second derivatives.doc

第1页：Excel 电位滴定练习数据表

第2页：一级微商数据的电子表格计算

• 38525.500.39626.000.42628.00Answer Wewillfirstenterthedataintothespreadsheetandconstructanordinarytitrationcurve.Enterthedatafromthetableaboveandusethe Chart Wizardtoplottheordinarytitrationcurveasshownin Figure1.ThisplotismadeasanXY(scatter)plot.Namethe Workbook,POTTITR.xlsandsaveit.Figure1.Nowwewillcomputethefirstderivative.Inordertomakeroomforthesetolineupwiththeappropriatevolumesletuscopythedata(columns Aand Bfrom Figure1)in to as epa rate sheet,Sheet2,leavingtheoriginaldataandplotin Sheet1.Now,in Sheet2,insertblankrowsbetweeneachpairofdatapointsasshownin Figure2.Labelcolumns C,D,E,and Fwith "[Delta]E, V", "[Delta]V, mL", "[Delta]E/[Delta]V, V/mL"and"[Delta]2E/[Delta]V2,V2/mL2"respectively.Thefirstderivativebetweenthe first two points (5.00 and 15.00 mL) is the difference in cell potential[Delta]E=(0.085-0.062)Vdividedbythedifferenceinvolume[Delta]V=(15.00-5.00)ml.ForcellC3,calculate[Delta]Eas=B4-B2andcopytheresultintotheoddnumberedcellsincolumn C(C3toC37).ForcellD3,calculate[Delta]Vas=A4-A2andlikewisecopytheformulainto

第3页：一级微商公式与单元格填充

theoddnumberedcellsincolumn D.IncellE3thefirstderivativeiscalculated as =C3/D3. This result is placed in cell E3 because itisassociatedwithavolumemidwaybetweenthefirsttwovolumepoints..Thissame formula can be copied into the other cells in column E.Figure2.Nowwewillcomputethesecondderivativeandentertheresultsincolumn F.Thesecondderivativecanbeestimatedasthechangein[Delta]Eperunitchangeinvolume.Hence,for the[Delta]EvaluesincellsE5andE3,the change in [Delta]E is (0.107-0.085)-(0.085-0.062) V. Thisisassociatedwithachangeinvolume[Delta]Vof(15.00-5.00)mL.Wecancomputethisin Sheet2as=(E5-E3)/(A4-A2).ThisformulaisplacedincellF4becauseitisthesecondderivativeassociatedwiththeaveragevolumeof15.00mL.Theresultingcalculationsshouldbeasshownin Figure2.Nowwemustpreparethefirstandsecondderivativeplots.Itisbesttoremovetheblankrowsbeforeplottingsothat Excelwillhavedataineachrow.Copythedataincolumns Aand Eof Sheet2intoanew Worksheet,Sheet3.Pastecolumn A,Sheet2intocolumn A,Sheet3.Pastecolumn E,Sheet2intocolumn C,Sheet3.Besuretouse Paste Specialandpastethevaluesonly.Forthefirstderivativeplot,thevolumesassociatedwitheachvalueofthederivativecanbecalculatedfromtheaverageof

第4页：平均体积列与微商曲线绘制

thetwovolumesusedtocomputethederivative.Thusforthefirstpointofthederivative,the average volume is(15.00+5.00)/2=10.00mL.Forthesecondpoint,the average is(20.00+15.00)/2=17.50mLandsoon.Entertheformula=Average(A2,A4)intocellB3andcopythisintotheblankcellsincolumn B.Namecolumn B"Mean Volume".Nowwewillremovethecellswithoutnumbersinthem.Arrangetoplotthedatausingthe Chart WizardandtheXY(scatter)plot.Theresultingchartshouldappearasin Figure3.Figure3.Thesecondderivativedatawillnowbecopiedintoanew Sheet4.Copy(Paste Special)thedataofcolumns Aand Ffrom Sheet2into Sheet4.Nowtheblankrowscanberemoveddirectlysincethesecondderivativedataalignwiththevolumes.Removetheblankrowsandredundantcolumnssothat Sheet4lookslike Figure4.

第5页：二阶微商曲线与终点读取

Figure4.Plotthesedatausingthe Chart Wizardtoobtaintheplotshownontherightsideofthefigure.Ifyouwouldliketodeterminetheendpointveryprecisely,youcanmanipulatetheaxestolocatetheequivalencepoint.Heretheendpointisseentobeapproximately24.33mL.Thiscouldhavealsobeendoneonthefirstderivativeplot,butitissomewhateasiertofindthezerocrossingthanitistofindthemaximum.*Courtesy Prof.S.R.Crouch.